Effects of curvature and gravity from flat spacetime

TL;DR

This paper explores gravity in flat spacetime through quantum tunnelling in Rindler space and develops a Poincare gauge theory, resolving symmetry issues with off-shell analysis and demonstrating the triviality of certain symmetries.

Contribution

It introduces a tunnelling framework for Unruh radiation and provides an off-shell gauge analysis to clarify Poincare symmetries in gravity theories.

Findings

Calculated thermal spectrum and temperature for accelerated observers.

Constructed off-shell gauge generators for Poincare symmetry.

Showed certain symmetries are trivial and do not affect physical states.

Abstract

We study some aspects of gravity in relation to flat spacetime. At first, we study an accelerated observer in Minkowski space as a quantum tunnelling problem in Rindler space. Both Bosonic and Fermionic modes are calculated to construct a reduced density matrix of particles tunnelling out across the accelerated Rindler horizon, giving a thermal spectrum characterized by a temperature proportional to the local acceleration - Unruh temperature. So, we calculate both the spectrum and temperature from within the tunnelling framework. In another direction, following Utiyama-Sciama-Kibble, we localise the Poincare group to obtain a Poincare gauge theory (PGT) of gravity. It had been pointed before in the literature, that the Poincare symmetries seemed to be recoverable canonically only on-shell. This would however mean existence of two independent sets of symmetries, each by itself having number of gauge parameters equal to the Poincare group, implying an apparent doubling of symmetries. To resolve this, we first start by a constraint analysis and construct the first-class gauge generator through an explicitly off-shell algorithm. We investigate both the Mielke-Baekler 3d model and a PGT formulation of New-Massive gravity. Next, we carefully study the symmetries and corresponding Noether identities to show that the difference between the two sets is a `trivial symmetry.' These is a transformation of fields that is not a true gauge symmetry as it gives rise to no new gauge degeneracy in defining physical states.